SUSY in the Sky with Gravitons

TL;DR

This work reveals a hidden $\mathcal{N}=2$ supersymmetry governing the gravitational scattering of two spinning compact bodies, valid up to quadratic-in-spin order in arbitrary dimensions. It develops a quadratic-in-spin extension of the worldline quantum field theory (WQFT) by embedding spin in an $\mathcal{N}=2$ supersymmetric worldline action and, where appropriate, incorporating finite-size corrections. From the $D$-dimensional eikonal phase $\chi$—the free energy of the WQFT—the authors derive the deflection, spin kick, and, for aligned spins, the scattering angle to 1PM and 2PM order, with explicit results in $D=4$ that agree with Kerr-based benchmarks. The framework unifies spinning-particle formalisms with amplitude-based and EFT approaches, provides a pathway to higher-spin and higher-PM generalizations, and highlights approximate SUSY as a guiding principle for conserving energy, SSC, and spin length even when finite-size effects are included.

Abstract

Picture yourself in the wave zone of a gravitational scattering event of two massive, spinning compact bodies (black holes, neutron stars or stars). We show that this system of genuine astrophysical interest enjoys a hidden $\mathcal{N}=2$ supersymmetry, at least to the order of spin-squared (quadrupole) interactions in arbitrary $D$ spacetime dimensions. Using the ${\mathcal N}=2$ supersymmetric worldline action, augmented by finite-size corrections for the non-Kerr black hole case, we build a quadratic-in-spin extension to the worldline quantum field theory (WQFT) formalism introduced in our previous work, and calculate the two bodies' deflection and spin kick to sub-leading order in the post-Minkowskian expansion in Newton's constant $G$. For spins aligned to the normal vector of the scattering plane we also obtain the scattering angle. All $D$-dimensional observables are derived from an eikonal phase given as the free energy of the WQFT, that is invariant under the $\mathcal{N}=2$ supersymmetry transformations.